Optimal Networks For Mass Transportation Problems

In the framework of transport theory, we are interested in the following
optimization problem: given the distributions $\mu^+$ of working people
and $\mu^-$ of their working places in an urban area, build a
transportation network (such as a railway or an underground system) which
minimizes a functional depending on the geometry of the network through a
particular cost function. The functional is defined as the Wasserstein
distance of $\mu^+$ from $\mu^-$ with respect to a metric which depends
on the transportation network.